Applying bounds to a probability distribution during simulation | Vose Software

# Applying bounds to a probability distribution during simulation

ModelRisk function: VoseXBounds(Min,Max)

ModelRisk function: VosePBounds(MinP,MaxP)

It is sometimes useful to run a Monte Carlo simulation using part of a known distribution for a random variable.

The functions above can be inputted as an extra parameter into distributions (after the U-parameter) and the result is a truncation of the distribution based on values (VoseXounds) or cumulative probabilities (VosePBounds).

## Example 1

The manufacturing process for a steel ring will introduce cracks with length of a known distribution of size given by a Weibull(2,3) mm distribution. However, a quality check on the ring will detect any cracks larger than 1.5mm. The remaining cracks can be modeled using:

VoseWeibull(2,3,,VoseXBounds(,1.5))

Note that the lower limit is left blank.

## Example 2

Wind gusts on an oil rig have speeds following a Lognormal(20,30) km/hour distribution. Thus, about 6% of wind speeds rise above 60km/hour. We want to investigate the effect of 60+ km/hour wind speeds on the design of the structure. Instead of simulating all wind speeds and ignoring 94% of the samples, we can use the truncated distribution:

Voselognormal(20,20,,VoseXBounds(60,))

## Example 3

People living near an industrial site are exposed on average to Lognormal(1.6, 3.3) mg of a chemical per day depending on the location of their house. We want to investigate the toxic effects of the 10% receiving the highest exposure. We can model this exposure using:

Voselognormal(1.6, 3.3,,VosePBounds(0.9, ))

## Allowed parameter combinations:

VoseXBounds(Min, Max) – truncates the distribution to lie between Min and Max

VoseXBounds(Min,) – truncates the distribution to lie above Min

VoseXBounds(Min) – truncates the distribution to above Min

VoseXBounds(,Max) – truncates the distribution to lie below Max

VoseXBounds() or VoseXBounds(,) – no truncation

VosePBounds(P, Q) – truncates the distribution to lie between the P*100 and Q*100 percentiles

VosePBounds(P,) or VosePBounds(P) – truncates the distribution to lie above the P*100 percentile

VosePBounds(,Q) – truncates the distribution to below the Q*100 percentiles

VosePBounds() or VosePBounds(,) – no truncation